Scene adaptive coders are constituted by the cascade of a linear transform, scalar quantization, entropy coding and a buffer controlled by a feedback loop for bit rate regulation. The main contribution of this paper is to derive an analytical criterion evaluating the performances of any perfect reconstruction linear transform in the frame of scene adaptive coding. This criterion is, thereafter, used in order to optimize linear multiresolution transforms. The optimization adapts the filters parameters to the codec features and to the statistics of the 2-D sources; so, the authors call these transforms adapted multiresolution transforms (AMTs). The transforms under study are implemented by a cascade of separable perfect-reconstruction (PR) FIR two-band filter banks that can change at each resolution level. Two types of filter banks are envisaged: the PR orthogonal quadrature mirror filter (QMF) bank, which allows to implement the orthogonal AMT and the PR linear-phase filter (LPF) bank, which implements the biorthogonal AMT. They perform the optimization of the filters in their factorized lattice form, taking the finite length of the multipliers into account. Their criterion also allows them to show the performances achieved by these two linear multiresolution transforms compared to other linear (multiresolution) transforms